# Daily Archives: January 5, 2016

## Burst Balloons

Problem source: https://leetcode.com/problems/burst-balloons/

Given n balloons, indexed from 0 to n-1. Each balloon is painted with a number on it represented by array nums. You are asked to burst all the balloons. If the you burst balloon i you will get nums[left] * nums[i] * nums[right] coins. Here left and right are adjacent indices of i. After the burst, the left and right then becomes adjacent.

Find the maximum coins you can collect by bursting the balloons wisely.

Note:
(1) You may imagine nums[-1] = nums[n] = 1. They are not real therefore you can not burst them.
(2) 0 ≤ n ≤ 500, 0 ≤ nums[i] ≤ 100

Example:

Given [3, 1, 5, 8]

Return 167

nums = [3,1,5,8] –> [3,5,8] –> [3,8] –>  –> []
coins = 3*1*5 + 3*5*8 + 1*3*8 + 1*8*1 = 167

Solution: This problem is a good exercise for dp.

First of all, we extend nums[] with 1 on each side. For example, we extend [3, 1, 5, 8] to [1, 3, 1, 5, 8, 1]. Let’s define dp[][]. dp[left][right] means the maximum value when we burst all balloons between nums[left] to nums[right](pay attention that balloons left and right are not included). For [1, 3, 1, 5, 8, 1], the result is dp. And we have dp formula: check my code on github: link